Research progress and prospect of numerical methods for modelling water hammer in hydraulic pipelines

【Objective】Water hammer in hydraulic pipelines is a critical hydraulic transient phenomenon that threatens the safe and stable operation of water conservancy and water supply systems. Numerical simulation is the key technical means for studying and predicting water hammer effects, but traditional methods have limitations in handling complex transient processes and ensuring simulation accuracy. This paper systematically reviews the research progress of numerical methods for simulating water hammer in hydraulic pipelines, analyse the application potential of high-precision numerical methods, and highlight the future research directions.【Method】Based on a comprehensive literature review, this review focused on principles, applications and advantages and disadvantages of the method of characteristics (MOC), finite difference method (FDM), and Godunov-based finite volume method (FVM) in one-dimensional pipeline modelling. Additionally, numerical experiments are conducted to explore the accuracy improvement of the weighted essentially non-oscillatory (WENO) method in simulating water hammer. 【Result】① Compared with MOC, FVM has more computationally accurate but has limited capability in capturing strong discontinuities during hydraulic transient processes. ② FVM integrated with the high-order WENO scheme can significantly improve simulation accuracy of pressure wave propagation and attenuation of water hammer. ③ Improved high-precision numerical methods provide an innovative solution to resolve the inherent limitations of traditional numerical method for water hammer simulation.【Conclusion】The FVM combined with high-order WENO scheme is potential for simulating water hammer. Future research should focus on exploring engineering applicability of high-resolution and robust numerical methods, with particular emphasis on investigating the integration of neural networks and traditional numerical approaches. This could lead to breakthroughs in improving the accuracy of water hammer modelling and safe operation of hydraulic pipeline systems.